When interest is compounded continuously, the amount of money increases at a rate proportional to the amount S present at time t, that is, dS/dt = rS, where r is the annual rate of interest. (a) Find the amount of money accrued at the end of 8 years when $9000 is deposited in a savings account drawing 52% annual interest compounded continuously. (Round your answer to the nearest cent.) $ (b) In how many years will the initial sum deposited have doubled? (Round your answer to the nearest year.) 12 years (c) Use a calculator to compare the amount obtained in part (a) with the amount S = 9000 1 + 8(4) that is accrued when interest is compounded quarterly. (Round your answer to the nearest cent.) :**....................: S = $ Enter a number.
When interest is compounded continuously, the amount of money increases at a rate proportional to the amount S present at time t, that is, dS/dt = rS, where r is the annual rate of interest. (a) Find the amount of money accrued at the end of 8 years when $9000 is deposited in a savings account drawing 52% annual interest compounded continuously. (Round your answer to the nearest cent.) $ (b) In how many years will the initial sum deposited have doubled? (Round your answer to the nearest year.) 12 years (c) Use a calculator to compare the amount obtained in part (a) with the amount S = 9000 1 + 8(4) that is accrued when interest is compounded quarterly. (Round your answer to the nearest cent.) :**....................: S = $ Enter a number.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:When interest is compounded continuously, the amount of money increases at a rate proportional to the amount S present at time t, that is, dS/dt = rS, where r is the annual
rate of interest.
(a) Find the amount of money accrued at the end of 8 years when $9000 is deposited in a savings account drawing 52% annual interest compounded continuously. (Round
4
your answer to the nearest cent.)
$
(b) In how many years will the initial sum deposited have doubled? (Round your answer to the nearest year.)
12
years
(c) Use a calculator to compare the amount obtained in part (a) with the amount S = 9000 1 + (0.0575)
8(4)
that is accrued when interest is compounded quarterly.
4
(Round your answer to the nearest cent.)
S = $
Enter a number.
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